To find the acceleration of the system and the tension in the string, we can use Newton's second law of motion and consider the forces acting on each block.
Let's assume that the positive direction is upward. In this case, the gravitational force acting on block m1 is m1 * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). The gravitational force acting on block m2 is m2 * g.
Now, let's consider the tension in the string. Since the string is massless and assuming it does not stretch, the tension is the same on both sides of the pulley. Let's call the tension in the string T.
For block m1: The net force acting on m1 is T (upward tension) minus the gravitational force, m1 * g (downward force). So we can write: T - m1 * g = m1 * a, where a is the acceleration of the system.
For block m2: The net force acting on m2 is the gravitational force, m2 * g (downward force) minus T (upward tension). So we can write: m2 * g - T = m2 * a.
Since the blocks are connected by the string, they have the same acceleration (a) in magnitude but opposite in direction.
Now we can solve the system of equations: T - m1 * g = m1 * a m2 * g - T = m2 * a
Adding these two equations, we get: T - m1 * g + m2 * g - T = m1 * a + m2 * a m2 * g - m1 * g = (m1 + m2) * a
Simplifying further: g * (m2 - m1) = (m1 + m2) * a
Finally, we can find the acceleration of the system: a = g * (m2 - m1) / (m1 + m2)
Substituting the given masses: a = 9.8 m/s^2 * (3 kg - 2 kg) / (2 kg + 3 kg) = 9.8 m/s^2 / 5 = 1.96 m/s^2
The tension in the string can be found by substituting the value of acceleration (a) into either of the original equations: T = m1 * g + m1 * a T = 2 kg * 9.8 m/s^2 + 2 kg * 1.96 m/s^2 T = 19.6 N + 3.92 N T ≈ 23.52 N
So, the acceleration of the system is approximately 1.96 m/s^2, and the tension in the string is approximately 23.52 N.